All solutions of the equation x²+x+1 = yz in non-negative integers x,y,z are given in terms of an arithmetic continued fraction.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8,
author = {A. Schinzel},
title = {On the diophantine equation x$^2$+x+1 = yz},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {243-248},
zbl = {06487241},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8}
}
A. Schinzel. On the diophantine equation x²+x+1 = yz. Colloquium Mathematicae, Tome 139 (2015) pp. 243-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8/